△TUV

Question

is isosceles, with ∠T≅∠V
and m∠U=54°
. What is m∠T
?(1 point)
Responses

m∠T=63°
m angle upper T equals 63 degrees

m∠T=126°
m angle upper T equals 126 degrees

m∠T=36°
m angle upper T equals 36 degrees

m∠T=54°

Answer 1

In triangle \( \triangle TUV \), since it is isosceles with \( \angle T \cong \angle V \), we let \( m\angle T = m\angle V = x \).

We know that the sum of the angles in a triangle is \( 180^\circ \):

\[ m\angle T + m\angle U + m\angle V = 180^\circ \]

Substituting the known values into the equation, we have:

\[ x + 54^\circ + x = 180^\circ \]

This simplifies to:

\[ 2x + 54^\circ = 180^\circ \]

Subtracting \( 54^\circ \) from both sides gives:

\[ 2x = 126^\circ \]

Dividing by 2 to solve for \( x \):

\[ x = 63^\circ \]

Thus, \( m\angle T = 63^\circ \).

So the correct response is:

m∠T = 63°.